Fair Division in Theory and Practice
[CSE/Poli Sci 245A (Spring 2015)]

Pick just one question from this web page to address in your group. Or come up with your own but ask us about that first.

Questions using dataset 1

1. Using population data from the 50 states following several different censuses, allocate seats using different apportionment methods. Measure the proportionality of these different allocations using several different indices of proportionality. Which states do better/worse under different methods?
2. Look at several presidential elections. Using the census data provided for 1980, 1990, 2000, and 2010 reallocate House seats using a few different methods. The electors that a state is apportioned is the number of Representatives plus the number of Senators. D.C. always has the number of electors of the state with the least number of electors (usually three). Using these different apportionments, determine if different methods would have led to different presidential election outcomes.
3. Using population data from a particular census and our current method of apportionment (Hill’s method), could any states be made better off by merging or splitting in terms of their final seat allocations? (To make your problem easier, start by considering the smallest and largest states.)
4. How would seat allocations change if Washington D.C. was granted representation in the House? If Hamilton’s method was used to apportion seats, would the addition of Washington D.C. create an apportionment paradox (if, for example, the size of the House was increased by 1 seat for D.C.)?

   Questions using dataset 2

5. Consider the election data at the state level and devise a proportional representation system that might work for the United States. For example, all House seats within a state could be allocated based on some PR, and the Senate could act as compensatory seats to either increase proportionality by party representation or by state representation. How does your approach work? What are the advantages/disadvantages of your approach?
6. In terms of the partisan composition of a state, we can think of proportionality of electoral outcomes or of district composition. For example, individual districts might be proportional if they mirror the composition of the state, while outcomes are proportional if seats are allocated proportionally to the parties across the state. How would you measure proportionality of each type? What is the relationship between these two types of proportionality?